The invention concerns a method for automatically determining the quantitative composition of a powder sample, which consists of different phase contents of crystalline and/or amorphous phases, from a diffraction diagram recorded by diffractometry from the powder sample or from an energy-dispersive spectrum, the method comprising the following steps:
(a) predetermining a list of phases which are to be allocated to the phase contents in the powder sample;
(b) calculating a theoretical diffraction diagram or theoretical energy-dispersive spectrum based on the phases predetermined in the list in step (a);
(c) fitting the theoretical diffraction diagram or theoretical energy-dispersive spectrum to that of the recorded powder sample by variation of the phase contents of the theoretical diffraction diagram or theoretical energy-dispersive spectrum.
A method of this type is disclosed in an article by Hill R J, Howard C J [1].
I. C. Madsen and N. V. Y. Scarlett [2] give an up-to-date overview of powder-diffractometric methods for quantitative phase analysis.
X-ray diffractometry is used in a plurality of ways for analyzing crystalline (and with certain restrictions also amorphous) components of samples. X-ray radiation is thereby diffracted on crystal planes in the sample. The spatial intensity distribution of the diffracted X-ray radiation, in particular, the position of intensity maxima (“reflexes”) gives information e.g. about interlattice plane distances and therefore about the crystal lattice (lattice symmetry) or also about preferred interlattice plane orientations (textures). The basic relationship between interlattice plane distance, angle of incidence and wavelength of X-ray radiation is described by Bragg's law. Procedures based on the Rietveld method are often used for quantification in measurements by X-ray diffractometry. The Rietveld method adjusts a theoretically calculated X-ray diffraction diagram of a polycrystalline substance to a measured X-ray diffraction diagram by means of the mathematical method of least squares. The crystal structure, i.e. the spatial arrangement of the atoms of all existing phases, is required for calculating, in particular, the reflex intensities in the X-ray diffraction diagram. More recent methods based on adjustment of a) individual reflexes, b) the Pawley method or c) the LeBail method use measured intensities instead of calculated intensities, which can be obtained e.g. from measurement of a pure phase (e.g. PONKCS method [3]. This enables quantification of phases, the crystal structure of which is only partially known or not known at all (e.g. amorphous phases).
However, all methods for quantitative analysis of powder samples disclosed up to now only enable quantification of phases which are actually present in the sample. If, however, the refinement model specifies phases which are actually not present in the sample, one still finds phase contents (often >>1%) either as a result of parameter correlations (i.e. inadmissible allocation of intensities to the non-existing phase) or through accidental adjustment of artifacts such as e.g. noise or other profile misfits.
For this reason, the problem arises that the exact qualitative composition of the sample must be known prior to the quantitative analysis.
This causes problems when the composition of the sample fluctuates, e.g. in case of samples from a quarry.
The quantitative analysis therefore requires a pre-scan, wherein, however, for example due to noise, phases are also found which are actually not present in the sample.
It is therefore the underlying purpose of the invention to enable automatic exclusion of amorphous or crystalline phases with phase contents below a user-definable threshold value in profile adjustment methods based on the Rietveld or Pawley methods.